Addition Problems: Step-by-Step Solutions

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Hey guys! Today, we're going to tackle some addition problems together. We'll break them down step-by-step so you can easily follow along. Addition is one of the fundamental operations in mathematics, and mastering it is crucial for more advanced topics. So, let's dive in and get those numbers adding up!

Problem 1: Adding Multiple Numbers

Our first problem looks like this:

304 285 + 56 140 + 84 203 = ?

When we have multiple numbers to add, it’s best to take it one step at a time. We can start by adding the first two numbers and then adding the result to the third number. Here's how we can do it:

Step 1: Add the First Two Numbers

Let’s add 304 285 and 56 140. Remember to align the numbers properly by their place values (ones, tens, hundreds, etc.).

  304 285
+  56 140
----------

Now, let's add each column starting from the right (ones place):

  • 5 + 0 = 5
  • 8 + 4 = 12 (Write down 2 and carry over 1)
  • 2 + 1 + 1 (carried over) = 4
  • 4 + 6 = 10 (Write down 0 and carry over 1)
  • 0 + 5 + 1 (carried over) = 6
  • 3 + 0 = 3

So, the result of 304 285 + 56 140 is 360 425.

Step 2: Add the Result to the Third Number

Now, we need to add 360 425 to the third number, which is 84 203.

  360 425
+  84 203
----------

Again, let's add each column starting from the right:

  • 5 + 3 = 8
  • 2 + 0 = 2
  • 4 + 2 = 6
  • 0 + 4 = 4
  • 6 + 8 = 14 (Write down 4 and carry over 1)
  • 3 + 0 + 1 (carried over) = 4

So, the final result of 304 285 + 56 140 + 84 203 is 444 628.

Therefore,

304 285 + 56 140 + 84 203 = 444 628

Problem 2: Multiplication and Addition

Next up, we have a problem that involves both multiplication and addition:

1 * 7 + 2 * 73 = ?

Remember, guys, that when we have a combination of operations, we need to follow the order of operations (often remembered by the acronym PEMDAS/BODMAS):

  1. Parentheses/Brackets
  2. Exponents/Orders
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

In this case, we have multiplication and addition, so we'll do the multiplication first.

Step 1: Perform the Multiplications

We have two multiplication operations:

  • 1 * 7 = 7
  • 2 * 73 = ?

Let's calculate 2 * 73:

   73
*  2
----
  146

So, 2 * 73 = 146

Step 2: Perform the Addition

Now we add the results of the multiplications:

7 + 146 = ?

   146
+  7
----
  153

So, the final result of 1 * 7 + 2 * 73 is 153.

Therefore,

1 * 7 + 2 * 73 = 153

Problem 3: Another Multi-Digit Addition

Let's try another multi-digit addition problem:

3 * 4 9 +
1 1 3 8 *
1
*
1
*
4
****+
879*
3 2 2 4 9

This problem looks a bit jumbled, but I believe it can be written like this, focusing on the core addition:

349 + 1138 + 1 + 1 + 4 + 879 + 32249 = ?

We have several numbers to add here, so let’s take it step by step. It is always great to rewrite the addition in a clear column format.

Step 1: Align the Numbers

First, let's align the numbers vertically by their place values:

   349
  1138
     1
     1
     4
   879
+32249
------

Step 2: Add the Numbers Column by Column

Now, let’s add each column, starting from the right (ones place):

  • 9 + 8 + 1 + 1 + 4 + 9 + 9 = 41 (Write down 1 and carry over 4)
  • 4 + 3 + 0 + 0 + 0 + 7 + 4 (carried over) + 4 = 22 (Write down 2 and carry over 2)
  • 3 + 1 + 0 + 0 + 0 + 8 + 2 (carried over) + 2 = 16 (Write down 6 and carry over 1)
  • 0 + 1 + 0 + 0 + 0 + 0 + 2 (from 32249) + 1 (carried over) = 4
  • 0 + 0 + 0 + 0 + 0 + 0 + 3 = 3
   349
  1138
     1
     1
     4
   879
+32249
------
 34621

So, the result of 349 + 1138 + 1 + 1 + 4 + 879 + 32249 is 34621.

Therefore,

349 + 1138 + 1 + 1 + 4 + 879 + 32249 = 34621

Problem 4: Addition with Larger Numbers

Our final problems involve adding larger numbers:

+ 2 700 = ?
+ 489 700 = ?

I suspect there's a missing number or context here. I think we might be looking at an incomplete addition expression. It seems like these are meant to be separate problems, but we need something to add 2700 and 489700 to. If we assume there's a missing initial value of zero, we can complete the additions like this:

Step 1: Complete First Addition

0 + 2700 = ?

This one is pretty straightforward. Adding zero to any number gives you that number.

   0
+2700
-----
 2700

So,

0 + 2700 = 2700

Step 2: Complete Second Addition

0 + 489700 = ?

Again, adding zero to any number results in that number itself.

       0
+ 489700
--------
 489700

So,

0 + 489700 = 489700

Final Thoughts

Great job, guys! We've worked through several addition problems today, from simple multi-number addition to problems involving multiplication and even a bit of number alignment. Remember to take your time, align your numbers carefully, and follow the order of operations. With practice, you'll become addition superstars! Keep up the great work! If you have more problems or questions, feel free to ask!